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A309189 (1/10) times the number of n-member subsets of [10n] whose elements sum to a multiple of n.

%I A309189 #11 Jul 20 2019 08:10:35
%S A309189 1,9,136,2289,42376,834336,17125354,362345361,7847250409,173103073384,
%T A309189 3875837737520,87857163416064,2012268157890524,46497242493163450,
%U A309189 1082614775186919136,25374686712458407441,598217593341171422090,14176230568946364963825
%N A309189 (1/10) times the number of n-member subsets of [10n] whose elements sum to a multiple of n.
%C A309189 Also (1/9) times the number of n-member subsets of [10n-1] whose elements sum to a multiple of n.
%H A309189 Alois P. Heinz, <a href="/A309189/b309189.txt">Table of n, a(n) for n = 1..712</a>
%F A309189 a(n) = 1/(10n) * Sum_{d|n} binomial(10d,d)*(-1)^(n+d)*phi(n/d).
%p A309189 with(numtheory):
%p A309189 a:= n-> add(binomial(10*d, d)*(-1)^(n+d)*
%p A309189         phi(n/d), d in divisors(n))/(10*n):
%p A309189 seq(a(n), n=1..25);
%o A309189 (PARI) a(n) = 1/(10*n) * sumdiv(n, d, binomial(10*d, d)*(-1)^(n+d)*eulerphi(n/d)); \\ _Michel Marcus_, Jul 20 2019
%Y A309189 Column k=10 of A309148.
%K A309189 nonn
%O A309189 1,2
%A A309189 _Alois P. Heinz_, Jul 15 2019